He described it as â€œanother kick in the teethâ€� for the people of Wales, not long after the government â€œrenegedâ€� on the electrification of the train line west of Cardiff.
On Monday, MPs were told that negotiations on Wylfa Newydd have started.
The news has been heralded as a major step forward for the scheme – which could be financed by public money.
Mr Jones said the Welsh Government should be involved with future talks.
He said: “The Wylfa Newydd project has the potential to transform the Welsh economy.
“It is vital that the Welsh Government has a seat at the table as the project progresses to the next stage and I will continue to press for this.
“The decisions made at a UK and Japan level will have a direct impact on Wales and we expect the UK government to work more closely with us to ensure that every opportunity is realised from this huge project in order to secure lasting benefits for Wales.”
The proposals feature a plant with a capacity of generating 2,700 megawatts of electricity, enough power for about five million homes.
The UK government said while a decision on the project’s go-ahead has not been made, it insisted the negotiations with developers Horizon Nuclear Power and the Japanese government was important step.
Among the key issues will be how much public money and state support will be ploughed into the plant.
During his address in the House of Commons, UK energy secretary Greg Clark did not comment on speculation that a guaranteed price for the electricity generated at Wylfa Newydd would be less than the “strike price” for the Hinkley Point C nuclear power station being built in Somerset.
Arguably the difference between the Swansea Bay Tidal Lagoon and Wylfa Newydd project is that whereas the former would meet the energy needs of Wales the latter would meet the Ned’s of the English Midlands.
Also whilst the Swansea project could see investors in other industries being attracted to that area, a Nuclear Power Plant and its dangers could well put investors of.
And there are dangers despite claims that it is safe.
Why do you think that it is that Nuclear Power Plant’s are built do far away from major population centres?Why not build one outside Birmingham or London?
The argument about the need for solid bases in the event of seismic activity seems a bit dubious as we don’t get many major earthquakes in these Islands .
Whatever the argument,it is London who decide which energy plants are built in in Wales and it is a bit late for our Third Rate Minister to demand a seat at the table, where his contribution will be minimal unless they send him to get the tea or coffee.